In figure, AB||DE, AB=DE, AC||DF and AC=DF. Prove that BC||EF and BC=EF.

Explanation

Given In figure AB||DE and AC||DF, also AB=DE and AC=DF
To prove `" "BC||EF and BC=EF`
Proof In quadrilateral ABED,
`" "AB||DE and AB=DE`
So, ABED is a parallelogram.
`therefore" "AD||BE and AD=BE" "...(i)`
Now, in quadrilateral ACFD,
`" "AC||FD and AC=FD`
Thus, ACFD is a parallelogram.
`therefore" "AD||CF and AD=CF" "...(ii)`
From Eqs. (i) and (ii),
`" "AD=BE=CF and CF||BE" "...(iii)`
Now, in quadrilateral BCFE,
`" "BE=CF" "`
and `" "BE||CF" "` [from Eq. (iii)]
So, BCFE is a parallelogram.
`therefore" " BC=EF and BC||EF " "` Hence proved.